Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x - 5$ and $ KL = 3x - 8$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x - 5} = {3x - 8}$ Solve for $x$ $ -x = -3$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({3}) - 5$ $ KL = 3({3}) - 8$ $ JK = 6 - 5$ $ KL = 9 - 8$ $ JK = 1$ $ KL = 1$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {1} + {1}$ $ JL = 2$